Abstract
We propose a deformation principle of gauge theories in three dimensions that can describe topologically stable self-dual gauge fields, i.e., vacua configurations that in spite of their masses do not deform the background geometry and are locally undetected by charged particles. We interpret these systems as describing boundary degrees of freedom of a self-dual Yang-Mills field in 2 + 2 dimensions with mixed boundary conditions. Some of these fields correspond to Abrikosov-like vortices with an exponential damping in the direction penetrating into the bulk. We also propose generalizations of these ideas to higher dimensions and arbitrary p-form gauge connections.
Highlights
We propose a deformation principle of gauge theories in three dimensions that can describe topologically stable self-dual gauge fields, i.e., vacua configurations that in spite of their masses do not deform the background geometry and are locally undetected by charged particles
An example of them is the deformation of the Chern-Simons theory, which turns out to be equivalent to the higher derivative Chern-Simons theory of [8] with tuned parameters
In three dimensions the deformation consists of a non-trivial gauge field redefinition, A → AΘ := A + Θ ⋆ F, F := dA + A ∧ A, (6.1)
Summary
The Rosenfeld energy-momentum tensor obtained from the variation of the action with respect to the background metric, ignoring boundary terms, is given by δ δgμν. For self-dual solutions, equation (2.13) and ΥΘ[Asd] = 0 hold, the deformed energy-momentum tensor (2.21) vanishes, δ δgμν. The self-dual solution of the deformed theory do not source gravity, in the sense that the field equations for the spacetime metric gμν will be the same as in the trivial vacuum A = 0. It is straightforward to see that the Feynman statistical weight constructed with the deformed action takes the same values for the trivial and for self-dual configurations, exp(iSΘ[A])|A=0 = exp(iSΘ[A])|A=Asd = 1. The vacua of a deformed system can be either voided or filled by self-dual electromagnetic fields, where they could appear as forming magnetic domains This feature may be of use for the description of two dimensional layers of materials exhibiting spontaneous magnetization
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